Heisenberg-Langevin Formalism for Open Circuit-QED Systems

Abstract
Major efforts in the field of quantum information and computation have been placed into the efficient manipulation and storage of quantum information in a quantum bit (qubit). These quantum operations are achieved via sending light signals through waveguides coupled to the qubit. However, the state of the qubit is commonly deduced indirectly through measuring the output waveguide signal. Therefore, it is required to have a formalism that connects the measured output signal to the effective dynamics of the qubit. The existing computational formalism, known as the input-output formalism, employs simplifying approximations without accounting for the distinct features of light-matter interaction from one device to the other. In my dissertation, I have derived a generalized input-output formalism, called Heisenberg-Langevin, without employing any of these approximations, as well as incorporating unique features of the interaction within a certain device. Hence, this formalism is applicable to a broader range of circuit-QED architectures and is valid in all different regimes of light-matter interaction, where previous models would break down.

Moreover, the main superiority of a quantum computer with respect to its classical counterpart lies in the unique computational operations that are allowed in the quantum world. In order for a device to perform these operations, it needs to maintain its “quantumness”, also referred to as “coherence”. Engineering such quantum devices is very challenging, since unwanted coupling to the surrounding environment fades the coherence away and the device collapses to the classical realm again. The time it takes for a quantum system to lose its coherence is called the coherence time. Importantly, previous theoretical attempts at calculating this quantity encountered an anomalous result, namely a divergent expression in the number of system modes, and hence used multiple approximations to resolve it. I have first demonstrated that the divergence is not an intrinsic anomaly, but is rather the result of employing phenomenological models that neglect an important feature of the light-matter interaction. Secondly, as a case study, I have applied the Heisenberg-Langevin formalism and provided a systematic procedure for the calculation of this quantity without encountering the problem of divergence.